ENGG2500 Chap.7 Internal Flow and the Moody Chart
Internal Flow and the Moody Chart
Internal flow develops from the entrance until its profile becomes fully developed. Reynolds number classifies the balance of inertia and viscosity. Fully developed laminar circular-pipe flow has an analytical Darcy friction factor, while turbulent resistance depends on Reynolds number and relative roughness and is read from a correlation or Moody chart. Darcy-Weisbach then converts resistance into head loss.
Profile shape links the no-slip wall to section-average velocity, and the correct property values, friction-factor convention and development assumption must travel with every pressure-drop calculation.
What this chapter covers
- 01
Entrance length and developed flow
- 02
Laminar and turbulent profiles
- 03
Reynolds classification
- 04
Relative roughness
- 05
Moody chart reading
- 06
Darcy-Weisbach major loss
Worked example · free
Major loss in a small pipe
- 1Convert flow and area for speed 0.815 m/s. The marks here are not a university mark allocation.
- 1Compute Reynolds number about 20,300.
- 1Classify the flow as turbulent.
- 1Darcy-Weisbach gives 0.520 m head loss.
Key terms
- Developed flow
- Fully developed flow has a profile shape that no longer changes downstream.
- Relative roughness
- Relative roughness is wall roughness divided by pipe diameter.
- Moody chart
- The Moody chart relates Darcy factor to Reynolds number and relative roughness.
- Darcy factor
- The Darcy factor is the resistance coefficient used in Darcy-Weisbach loss.
Internal Flow and the Moody Chart FAQ
Why does turbulent friction depend on roughness?
Turbulent mixing brings momentum toward the wall, where roughness elements disturb the near-wall flow. Their effect depends on size relative to pipe diameter and viscous scales. The Moody chart therefore uses both Reynolds number and relative roughness rather than one universal turbulent factor.
What is the difference between Darcy and Fanning factors?
They are two conventions for representing wall resistance. The Darcy friction factor is four times the Fanning factor. Darcy-Weisbach uses the Darcy definition, so mixing a Fanning value into that equation creates a result wrong by a factor of four.
How do I read a Moody chart?
Calculate Reynolds number and relative roughness first. Enter at the Reynolds number, move to the correct roughness curve and read the Darcy friction factor. In laminar circular-pipe flow, use sixty-four divided by Reynolds number instead of reading a turbulent curve.
What does fully developed flow mean?
Fully developed means the nondimensional velocity-profile shape no longer changes with downstream distance. Pressure can continue to fall, and fluid keeps moving, but the wall boundary layers have filled the pipe. Entrance-region correlations should be used when the available length is too short for that condition.
Why is average velocity used in Darcy-Weisbach?
Darcy-Weisbach is formulated with the cross-section average velocity, which is discharge divided by area. A centreline measurement is different and depends on profile shape. Convert any local measurement through a justified profile relation before treating it as the average speed in Reynolds number or head loss.
How does temperature affect a pipe-loss result?
Temperature changes viscosity and sometimes density, shifting Reynolds number and the friction factor even when geometry and flow rate stay fixed. Use properties at the stated operating temperature, classify the resulting regime and then choose the factor. A remembered room-temperature viscosity can put the calculation on the wrong chart branch.
When is a pipe hydraulically rough?
A turbulent pipe is hydraulically rough when roughness elements protrude through the viscous near-wall layer enough that friction becomes largely independent of Reynolds number. Relative roughness then controls the fully rough limit. The same physical pipe can behave smooth at one operating condition and rough at another.
Why can diameter dominate pipe design?
For fixed discharge, increasing diameter lowers average velocity as well as the length-to-diameter ratio in Darcy-Weisbach. Because velocity head contains speed squared, the combined reduction can be strong. A modest diameter change may therefore reduce pumping energy far more than a similar percentage change in straight-pipe length.
Exam move
Use one resistance worksheet for every pipe. Convert diameter and discharge to SI units, calculate area and average speed, then evaluate Reynolds number with properties at the operating temperature. Identify laminar, transitional or turbulent behaviour before selecting a friction relation. For turbulent flow, calculate relative roughness and read a Darcy friction factor from the Moody chart with both inputs visible.
Label the factor as Darcy so it cannot be confused with the Fanning definition. Apply Darcy-Weisbach with length, diameter and velocity head, and convert head loss to pressure drop only at the end. In iterative unknown-flow problems, guess the factor, solve for speed, recompute Reynolds number and repeat until the factor and flow agree.
Compare centreline and average velocity for one laminar and one turbulent profile, and note whether the measurement section is far enough from the entrance to justify a developed-flow model. Finish with a sign and scale check: loss must be positive and should rise with length and speed.